Isoparametric curves
are lines running along the surface in the U and V directions, showing
the shape of the surface as defined by the CVs.

Alias draws a NURBS
surface as a mesh of curves, called isoparametric curves, running
in the U and V directions.

Isoparametric curves
are sometimes called isoparms.

Unfortunately, the term
“isoparametric curve” is used to describe two related but subtly different
features of a surface:

Edit point isoparametric
curves

A line of constant parameter
at an edit point. The isoparametric curves at edit points are special,
since they represent the boundaries between “patches”. Like CVs, these isoparametric curves are
important in representing the surface within the system.

Alias draws these
types of isoparametric curves using solid lines.

This is the type of isoparametric curve
created by the Insert tool. Adding this type
of isoparametric curve actually changes the geometry of the surface.

You can only delete isoparametric curves
of this type.

Using this definition, a surface has
the same number of isoparametric curves in the U and V directions
as it has edit points.

Descriptive isoparametric
curves

Any line of constant
parameter in either U or V. For example, if you join
together every point on the surface where U=1.5, the resulting line
is a U isoparametric curve:

Alias draws these
types of isoparametric curves using dotted lines.

You can increase the number of this type
of isoparametric curve that is drawn for a surface with the Patch
precision tool.

Using this definition, a surface has
an infinite number of isoparametric curves.

You can use these isoparametric curves
to help you understand the surface shape, but the system doesn’t
use them to represent the surface internally.